US4071797A - Quartz piezo-electric element vibrating in a coupled mode - Google Patents

Quartz piezo-electric element vibrating in a coupled mode Download PDF

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Publication number
US4071797A
US4071797A US05/650,643 US65064376A US4071797A US 4071797 A US4071797 A US 4071797A US 65064376 A US65064376 A US 65064376A US 4071797 A US4071797 A US 4071797A
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United States
Prior art keywords
resonator
mode
thickness
ratio
width
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Expired - Lifetime
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US05/650,643
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English (en)
Inventor
Alphonse Ernst Zumsteg
Jean Engdahl
Raymond Huguenin
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Meggitt SA
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Societe Suisse pour lIindustrie Horlogere Management Services SA
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Priority to US05/650,643 priority Critical patent/US4071797A/en
Priority to GB53261/76A priority patent/GB1572810A/en
Priority to FR7639890A priority patent/FR2339197A1/fr
Priority to CH23177A priority patent/CH607450A5/xx
Priority to DE2701416A priority patent/DE2701416C3/de
Priority to JP366577A priority patent/JPS5290289A/ja
Application granted granted Critical
Publication of US4071797A publication Critical patent/US4071797A/en
Assigned to DRYAN-FORDAHL TECHNOLOGIES S.A. reassignment DRYAN-FORDAHL TECHNOLOGIES S.A. ASSIGNMENT OF ASSIGNORS INTEREST. Assignors: SOCIETE SUISSE POUR L'INDUSTRIE HORLOGERE MANAGEMENT SERVICES S.A.
Assigned to VIBRO METER, S.A. B.P. reassignment VIBRO METER, S.A. B.P. ASSIGNMENT OF ASSIGNORS INTEREST. Assignors: DRYAN-FORDAHL TECHNOLOGIES SA, BY: BANKRUPTCY OFFICE, BIEL/BIENNE, BERN, SWITZERLAND
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
    • H03H9/15—Constructional features of resonators consisting of piezoelectric or electrostrictive material
    • H03H9/17—Constructional features of resonators consisting of piezoelectric or electrostrictive material having a single resonator
    • H03H9/19—Constructional features of resonators consisting of piezoelectric or electrostrictive material having a single resonator consisting of quartz
    • G—PHYSICS
    • G04—HOROLOGY
    • G04F—TIME-INTERVAL MEASURING
    • G04F5/00—Apparatus for producing preselected time intervals for use as timing standards
    • G04F5/04—Apparatus for producing preselected time intervals for use as timing standards using oscillators with electromechanical resonators producing electric oscillations or timing pulses
    • G04F5/06—Apparatus for producing preselected time intervals for use as timing standards using oscillators with electromechanical resonators producing electric oscillations or timing pulses using piezoelectric resonators
    • G04F5/063—Constructional details
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
    • H03H9/02—Details
    • H03H9/02007—Details of bulk acoustic wave devices
    • H03H9/02062—Details relating to the vibration mode
    • H03H9/0207—Details relating to the vibration mode the vibration mode being harmonic
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic elements; Electromechanical resonators
    • H03H9/02—Details
    • H03H9/02007—Details of bulk acoustic wave devices
    • H03H9/02157—Dimensional parameters, e.g. ratio between two dimension parameters, length, width or thickness

Definitions

  • quartz crystals of frequencies greater than 1 MHz have generally tended to be of a circular lens form and such forms suffer from various disadvantages including, of course, the problem of space occupation and the difficulty of manufacture including mounting. Accordingly, it was concluded that a rectangular form of quartz crystal would be much preferable, particularly where it was desired to use such a quartz as a resonator in a wrist watch. In such application the quartz resonator is subject to many problems not found in other applications. For example in view of a large variation of temperature it may be found necessary to provide arrangements for bringing about compensations and in any event it is desirable to provide a resonator having as flat a temperature characteristic as possible.
  • Such resonator should likewise provide high dynamic capacitance.
  • a high frequency quartz is to be used that such be of the AT-type in which, of course, as is well known principal vibrations occur in thickness shear.
  • an energy trapping arrangement may be provided whereby the ends of the rectangular bar are practically free of vibration and thus do not, in fact, influence the frequency of the portion of the crystal located between the electrodes.
  • the present invention goes a step further in providing an arrangement which takes into account temperature variations which affect the elastic constants, thereby modifying the thermal frequency coefficients.
  • the purpose of the invention is to provide a quartz resonator having such a selection of dimensional ratios length-to-width-to-thickness as will result in rectangular form resonators of very small width and employing the energy trapping principle, this latter being obtained either by an extra thickness of metallization or a thinning down of the outer extremities of the resonator through chemical attack, ion milling, etc. and for which the greatest dimensions will be found along the axis Z' , these ratios permitting the mastery of the behaviour in temperature variations, the obtaining of a dynamic capacity of maximum value, a high quality factor and a minimization of tolerance effects during manufacturing.
  • the invention accordingly provides a piezoelectric resonator cut from a quartz crystal in a rotated Y-cut of approximately 35°0' and having its greatest dimensions along Z' (YZW approximately equal 35° 0') arranged to vibrate in a mode which is the resultant of coupling of a thickness shear XY' mode and a flexural mode XY', the width-thickness ratio of the resonator being selected from certain ranges in accordance with the flexural harmonics.
  • the range may be between 1.1 and 1.9
  • the fourth flexural harmonic such ratio may be between 2.2 and 3.6.
  • Other ratios may likewise be chosen on a basis as shown hereinafter.
  • the resonator will be operated in an energy trapping mode and for this reason electrodes will be placed thereon confined to a small portion of the opposing surfaces between which the thickness shear vibrations normally take place.
  • FIG. 1 represents a rectangular resonator of the AT-cut having flat surfaces and the greatest dimension oriented along the X axis.
  • FIG. 2 represents a rectangular resonator of the AT-cut operating in the flexural mode XY' which propagates itself in the X direction and of which a portion of the energy in this mode is absorbed at the ends of the X axis or close to this axis.
  • FIG. 3 shows a rectangular resonator configuration of the AT-cut having convex surfaces and for which the greatest dimension is along the X axis.
  • FIG. 4 shows a resonator configuration according to the present invention for which the greatest dimension is along the Z' axis and the ratio of width to thickness is very small.
  • FIG. 5 shows a rectangular resonator according to the present invention wherein one may see how the flexural mode XY' vibrations end up on the free faces X which are no longer utilized for supporting the resonator.
  • FIG. 6 represents a rectangular resonator according to this invention which is held only at one extremity and for which the energy trapping zone is not necessarily midway along the length.
  • FIG. 7 is a diagram of normalized resonance frequencies of a rectangular resonator of the AT-cut as a function of the ratio a/b where a is the dimension along the X axis and b is the thickness.
  • the frequencies are normalized relative to the frequency f o , defined as ##EQU1##
  • C' 66 represents a shear modulus or coefficient around Z and ⁇ is representative of the density. Such a frequency would be that of an infinite plate.
  • FIG. 8 represents the frequency of resonance as a function of the temperature of one example of a rectangular resonator in accordance with the present invention.
  • FIG. 9 represents the linear temperature coefficient of the frequency at 25° C for rectangular resonators according to this invention.
  • FIG. 10 represents the dynamic capacity of rectangular resonators in accordance with the present invention.
  • FIG. 1 shows a quartz resonator in the AT-cut having a rectangular form with electrodes at the centre without convex surfaces and for which the greatest dimension, the length, is parallel to the X axis.
  • Such resonators have already been made having ratios a/b ⁇ 30.
  • Such resonators present two inconvenient features:
  • the ratio a/b must be greater than 30 in order to obtain a sufficient attenuation of the thickness shear vibrations between the electrodes and the edge of the resonator.
  • the flexural mode XY' which is coupled to the thickness shear and which is propagated in the direction X (see FIG. 2) is not subjected to the energy trapping arrangements and the fixing of the resonator on its ends will always absorb a portion of the flexural mode energy.
  • FIG. 3 shows a resonator configuration without electrodes having its length parallel to the axis X and which possesses two convex surfaces. These latter provoke a very substantial energy trapping which permits a reduction of the ratio a/b but at the same time necessitates a curved machining which is difficult and expensive.
  • shear vibrations XY' are always coupled to flexural vibrations in a plane XY'.
  • a flexural mode XY' is propagated in the direction X.
  • FIG. 8 represents a curve following such a calculation.
  • Such curves resemble those of the AT cut resonators but they are asymmetric and have a higher point of inflexion.
  • the lower point of inversion may be placed for example around 25° and the portion of the corresponding parabola is very open and extends at least to 50°.
  • This quadratic behaviour is very favourable to resonators which are required to work at ambient temperatures such as may be found for instance in a wrist-watch.
  • FIG. 9 gives the linear temperature coefficient of the frequency T f at 25° C as a function of the dimensional ratios and for different angles of cut.
  • Curves 2, 4, 6, 8, 10 and 12 are calculated for an angle of 35° 15', curve 6a for 34° 30' and curve 8a for 34° 36'.
  • Curves 4', 6', 8', 10' and 12' are measured for an angle of cut of 35° 15' and curve 4" for an angle of cut of 34° 48'.
  • Curves 6' and 10' are disturbed by the surface shear vibration which has not been taken into account by the theory. The agreement between theory and experience has proven to be quite good and especially so for the values of the ratio a/b corresponding to to the peaks of the curves. Such results seem to be new and show that T f depends in a parabolic and cyclic manner from the dimensional ratio a/b.
  • the value of the dynamic capacity C 1 depends equally in a parabolic and cyclic manner from the ratio a/b, FIG. 4.
  • Curves 4b, 6b, 8b, 10b and 12b represent measured values.
  • C 1 is maximum in the neighborhood of the values of the ratio a/b corresponding to the summits of the parabolas of T f .
  • This invention also provides the advantage that the energy trapping for coupled modes is much greater than that known up until the present time for simple modes. Rectangular resonators have been made without convex surfaces for a frequency of approximately 4.19 MHz with ratios c/b ⁇ 20 and a/b ⁇ 2.95 and which present a quality factor which is reproducible and greater than 500,000.
  • FIG. 4 shows the arrangement of the quartz related to its crystallographic axis in which c is the length and follows the Z' axis, a is the width and is along the X axis and b is the thickness and is along the Y' axis.
  • FIG. 5 is shown a mounted bar quartz which has been cut as shown in FIG. 4.
  • the centre electroding E across width a is such as to provoke a thickness shear type of vibration XY' coupled to a flexural vibration also XY'.
  • a thickness twist type of vibration may arise.
  • the energy trapping principle will apply so as to obtain an exponential diminution of this latter vibration towards the ends of the bar which are utilized as mounting points.
  • the zone of trapped energy be located in the centre of the bar according to its length and one may even arrange to fasten the bar at a single extremity.
  • the electrode zone E is in proximity to, even though somewhat separated from one end of the bar whereas the connecting electrodes are at the other end of the bar; as can be appreciated the bar can itself be mounted at one end. With this as in the FIG. 5 embodiment a very high quality factor is obtainable.

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  • Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • General Physics & Mathematics (AREA)
  • Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)
US05/650,643 1976-01-20 1976-01-20 Quartz piezo-electric element vibrating in a coupled mode Expired - Lifetime US4071797A (en)

Priority Applications (6)

Application Number Priority Date Filing Date Title
US05/650,643 US4071797A (en) 1976-01-20 1976-01-20 Quartz piezo-electric element vibrating in a coupled mode
GB53261/76A GB1572810A (en) 1976-01-20 1976-12-21 Quartz piezoelectric element vibrating in a coupled mode
FR7639890A FR2339197A1 (fr) 1976-01-20 1976-12-31 Element resonateur piezoelectrique a quartz vibrant dans un mode couple
CH23177A CH607450A5 (en)van) 1976-01-20 1977-01-10
DE2701416A DE2701416C3 (de) 1976-01-20 1977-01-14 Piezoelektrischer Schwinger in rechteckiger Blockform
JP366577A JPS5290289A (en) 1976-01-20 1977-01-18 Piezooelectric resonator

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US05/650,643 US4071797A (en) 1976-01-20 1976-01-20 Quartz piezo-electric element vibrating in a coupled mode

Publications (1)

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US4071797A true US4071797A (en) 1978-01-31

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US (1) US4071797A (en)van)
JP (1) JPS5290289A (en)van)
CH (1) CH607450A5 (en)van)
DE (1) DE2701416C3 (en)van)
FR (1) FR2339197A1 (en)van)
GB (1) GB1572810A (en)van)

Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4167686A (en) * 1973-12-21 1979-09-11 Hitohiro Fukuyo Miniaturized at-cut piezoelectric crystal resonator
FR2417886A1 (fr) * 1978-02-16 1979-09-14 Suisse Horlogerie Resonateur piezoelectrique
FR2440115A1 (fr) * 1978-10-24 1980-05-23 Philips Nv Resonateur piezoelectrique
EP0017103A1 (en) * 1979-03-27 1980-10-15 Dryan-Fordahl Technologies S.A. Coupled mode piezo-electric resonator
EP0019591A1 (de) * 1979-05-22 1980-11-26 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Quarzoszillator mit Temperaturkompensation
EP0032359A1 (de) * 1980-01-10 1981-07-22 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Oszillator mit digitaler Temperaturkompensation
US4320320A (en) * 1978-12-01 1982-03-16 Kabushiki Kaisha Suwa Seikosha Coupled mode tuning fork type quartz crystal vibrator
US4418299A (en) * 1977-01-12 1983-11-29 Kabushiki Kaisha Suwa Seikosha Face-shear mode quartz crystal vibrators and method of manufacture
US4525647A (en) * 1983-12-02 1985-06-25 Motorola, Inc. Dual frequency, dual mode quartz resonator
JPS6232627U (en)van) * 1985-08-12 1987-02-26
US6469423B2 (en) * 1993-10-18 2002-10-22 Seiko Epson Corporation Rectangular at-cut quartz element, quartz resonator, quartz resonator unit and quartz oscillator, and method of producing quartz element
US20030052743A1 (en) * 2000-01-10 2003-03-20 Piazza Silvio Dalla Device for producing a signal having a substantially temperature-independent frequency

Families Citing this family (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4076987A (en) * 1976-12-10 1978-02-28 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Multiple resonator or filter vibrating in a coupled mode
JPS5530286A (en) * 1978-08-25 1980-03-04 Seiko Instr & Electronics Ltd Thickness sliding flection crystal vibrator
JPS5530284A (en) * 1978-08-25 1980-03-04 Seiko Instr & Electronics Ltd Thickness sliding flection crystal vibrator
JPS5546633A (en) * 1978-09-28 1980-04-01 Seiko Instr & Electronics Ltd Thickness-sliding inflection crystal vibrator
JPS5577222A (en) * 1978-12-06 1980-06-10 Seiko Epson Corp Tuning-fork type vibrator
NL8000297A (nl) * 1980-01-17 1981-08-17 Philips Nv Piezoelektrische triller.
GB2124021A (en) * 1982-07-16 1984-02-08 Philips Electronic Associated Piezo-electric resonator or filter
JPS60214618A (ja) * 1984-04-10 1985-10-26 Nippon Dempa Kogyo Co Ltd 水晶振動子
JPS6236344Y2 (en)van) * 1986-05-29 1987-09-16

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2218200A (en) * 1934-06-02 1940-10-15 Bell Telephone Labor Inc Piezoelectric apparatus
US2306909A (en) * 1939-06-09 1942-12-29 Bell Telephone Labor Inc Piezoelectric crystal apparatus
US2321358A (en) * 1941-06-30 1943-06-08 Rca Corp Art of mounting piezoelectric crystals
US2574257A (en) * 1947-01-11 1951-11-06 Cambridge Thermionic Corp Method for manufacturing piezoelectric crystals free of conflicting modes of vibration

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2218200A (en) * 1934-06-02 1940-10-15 Bell Telephone Labor Inc Piezoelectric apparatus
US2306909A (en) * 1939-06-09 1942-12-29 Bell Telephone Labor Inc Piezoelectric crystal apparatus
US2321358A (en) * 1941-06-30 1943-06-08 Rca Corp Art of mounting piezoelectric crystals
US2574257A (en) * 1947-01-11 1951-11-06 Cambridge Thermionic Corp Method for manufacturing piezoelectric crystals free of conflicting modes of vibration

Cited By (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4167686A (en) * 1973-12-21 1979-09-11 Hitohiro Fukuyo Miniaturized at-cut piezoelectric crystal resonator
US4418299A (en) * 1977-01-12 1983-11-29 Kabushiki Kaisha Suwa Seikosha Face-shear mode quartz crystal vibrators and method of manufacture
FR2417886A1 (fr) * 1978-02-16 1979-09-14 Suisse Horlogerie Resonateur piezoelectrique
FR2440115A1 (fr) * 1978-10-24 1980-05-23 Philips Nv Resonateur piezoelectrique
US4320320A (en) * 1978-12-01 1982-03-16 Kabushiki Kaisha Suwa Seikosha Coupled mode tuning fork type quartz crystal vibrator
EP0017103A1 (en) * 1979-03-27 1980-10-15 Dryan-Fordahl Technologies S.A. Coupled mode piezo-electric resonator
US4245173A (en) * 1979-03-27 1981-01-13 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Beveled, coupled mode piezo-electric resonator
US4345221A (en) * 1979-05-22 1982-08-17 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Temperature compensated signal generator including two crystal oscillators
EP0019591A1 (de) * 1979-05-22 1980-11-26 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Quarzoszillator mit Temperaturkompensation
EP0032359A1 (de) * 1980-01-10 1981-07-22 Societe Suisse Pour L'industrie Horlogere Management Services S.A. Oszillator mit digitaler Temperaturkompensation
US4427952A (en) 1980-01-10 1984-01-24 Societe Suisse Pour L'industrie Horlogere Management Services Sa Oscillator circuit with digital temperature compensation
US4525647A (en) * 1983-12-02 1985-06-25 Motorola, Inc. Dual frequency, dual mode quartz resonator
JPS6232627U (en)van) * 1985-08-12 1987-02-26
US6469423B2 (en) * 1993-10-18 2002-10-22 Seiko Epson Corporation Rectangular at-cut quartz element, quartz resonator, quartz resonator unit and quartz oscillator, and method of producing quartz element
US20030052743A1 (en) * 2000-01-10 2003-03-20 Piazza Silvio Dalla Device for producing a signal having a substantially temperature-independent frequency
US6724266B2 (en) * 2000-01-10 2004-04-20 Eta Sa Fabriques D'ebauches Device for producing a signal having a substantially temperature-independent frequency

Also Published As

Publication number Publication date
FR2339197B1 (en)van) 1981-11-20
GB1572810A (en) 1980-08-06
FR2339197A1 (fr) 1977-08-19
CH607450A5 (en)van) 1978-12-15
DE2701416B2 (de) 1979-05-31
JPS5290289A (en) 1977-07-29
DE2701416A1 (de) 1977-07-28
DE2701416C3 (de) 1980-01-31

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Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:DRYAN-FORDAHL TECHNOLOGIES SA, BY: BANKRUPTCY OFFICE, BIEL/BIENNE, BERN, SWITZERLAND;REEL/FRAME:004762/0810

Effective date: 19870210